Study Of Rijke-type Thermoacoustic Instability By Using Modal Decomposition

In some devices,thermoacoustic instabilities refer to the appearance of pressure oscillation coupled with an unsteady heat release.Thermoacoustic instabilities can destroy the system of the gas turbine,but also is used to increase burning rate an reduce pollutant emissions of heavy fuel oils.The Rijke tube with two ends open consisted of a vertical pipe with a gauze(heated by a flame or electric).In the tube,strong acoustic oscillation is excited to study the thermoacoustic coupling mechanism,the vibration characteristics and its control method.In this paper,the horizontal placed Rijke tube with electric heating is built,to study the thermoacoustic instabilities.The wire is wound on the ceramic structure and heated by the power supply.The mean air flow is provided by a blower,and flow through the heater in the aluminum tube(Rijke pipe),excite the thermoacoustic oscillation in some conditions.The main experi-mental parameters such as the heater location xb/L,the air flow rate q and the heater power P affect the characteristics of the acoustic.The heater power determines the acoustic mode in the tube.The high heater power is good for exciting high-order modal acoustic at the right flow rate.These experimental parameters can be adjusted independently,and the air flow rate and heater power are collected average value.When the pressure vibration reach the limit cycle,the sensor at different positions in the tube measures the vibration pressure value of p(x,t),the acquisition time is 30s,and the frequency is 4096Hz.The results were analyzed by fourier decomposition,proper orthogonal decomposition and the combination of them.The vibration pressure values is measured in the tube X1=x/L=1/2,X2 =x/L=3/4 and X3=x/L=5/6,using the fourier decomposition to domain analysis,study the acoustic oscillation characteristic of different frequencies.The conclusion is that there are the fundamental and the second modal acoustic exist in the tube simultaneously,and the frequencies are f1=0.5c/L and f2=c/L,and the vibration pressure has the different frequency at the different positions Xn:the center of the tube X1 only to measure the acoustic oscillations with a frequency of f1,and X2 and X3 measure the acoustic frequency of f1 and f2.In the tube range x/L=0.015～0.98 installed within the 15 sensors,the sensor distance is△x/L 0.069,when using the proper orthogonal decomposition to study the spatial analysis,the results conclude the spatial functions ψn,the energy ratio λn,the phase an and the recon-structed pressure pn(x,t),thus the vibration characteristic of different wavelengths acoustic in the tube is studied,and the slight vibration which is hidden in the.total flow is shown.Combine proper orthogonal decomposition with fourier decomposition can be used to study the acoustic oscillations of different wavelengths and different frequencies in the tube.The method is that the modal coefficients an by fourier decomposition,bandpass filtering and in-verse Fourier decomposition to compute nine reconstructed pressure pn,m with different mode and different frequency.There are three different types vibration in the Rijke tube,type I is the acoustic wave with a wavelength of 2L,the energy ratio is no less than 85%in the total flow and plays a leading role;type II is the acoustic wave with a wavelength of L,distribute in the first three modes n = 1,2,3 by proper orthogonal decomposition;type Ⅲ is the ’end effect’,that caused by the the acoustic wave with a wavelength of 2L,this oscillation phenomenon never been found in the previous study.The heater suppression the acoustic oscillations of wavelengths L and 2L in the upper half of the tube,and the suppression of the acoustic waves with wavelength L is more pronounced.In all experimental conditions,the acoustic vibration with the wavelength L is always stronger in the second half of the tube x/L>0.5 than the first half x/L<0.5.